- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# The class X student's school in krishnagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

**(i)** Taking $A$ as the origin, find the coordinates of the vertices of the triangle.

**(ii)** What will be the coordinates of the vertices of $∆PQR$, if $C$ is the origin?

Also, calculate the areas of the triangles in these cases. What do you observe?

"

Given:

The class X students school in krishnagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

To do:

We have to find :

(i) The coordinates of the vertices of the triangle.

(ii) The coordinates of the vertices of $∆PQR$, if $C$ is the origin and also, calculate the areas of the triangles in these cases. What do you observe.

Solution:

(i) Taking $A$ as the origin, the coordinates of the vertices of the $\triangle \mathrm{PQR}$ are $\mathbf{P}(4,6), \mathbf{Q}(3,2)$ and $\mathbf{R}(6,5)$.

(ii) Taking $\mathrm{C}$ as origin, the coordinates of the vertices of the $\triangle \mathrm{PQR}$ are $P(12,2), Q(13,6)$ and $R(10,3)$ Area of $\triangle \mathrm{PQR}$

$\mathrm{P}(4,6), \mathrm{Q}(3,2)$ and $R(6,5)$

Here, $x_{1}=4, y_{1}=6, x_{2}=3, y_{2}=2, x_{3}=6$ and $y_{3}=5$.

Area of $\triangle \mathrm{PQR}=\frac{1}{2}[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]$

$=\frac{1}{2}[4(2-5)+3(5-6)+6(6-2)]$

$=\frac{1}{2}[-12-3+24]$

$=\frac{1}{2}[-15+24]$

$=\frac{1}{2}(9)$

$=\frac{9}{2}$ Hence, the area of $\triangle \mathrm{PQR}$ is $\frac{9}{2}$ sq units.

We observe that the area of $\triangle \mathrm{PQR}$ remains the same with different vertices.

- Related Questions & Answers
- How to share x axes of two subplots after they have been created in Matplotlib?
- 5 tips for balcony gardening
- What are the types of variables a class can have in Java?
- What are the P class and NP class in TOC?
- Company X has estimated their demand levels of their product A
- Why are humans jealous of their neighbor's success?
- What is the importance of extracurricular activities in a student's life?
- Minimum positive integer value possible of X for given A and B in X = P*A + Q*B in C++
- What are the Types of Activity Ratio?
- Find the number of integers x in range (1,N) for which x and x+1 have same number of divisors in C++
- Execute a script when there have been changes to the anchor part of the URL in HTML?
- Have you ever been in a jail? If yes, what have you faced?
- Group the marks of a particular student from a table and display total marks in a separate column for each student?
- Match any string containing a sequence of N p's
- Fourier Transform of Rectangular Function
- How to plot the X-axis labels on the upper-side of the plot in R?